On the theory of liquid and solid He 3

Abstract

The object of the present paper is to develop quantitatively several features of the theory of the nuclear spin system in liquid and solid He 3, elaborated previously. The effect of the application of external pressure on the spin system will thus be described in a more rigorous way than heretofore. The attempt to correlate the various experimentally determined thermal properties of the compressed liquid from the standpoint of the theory of the spin system leads one to recognize the need of new and precise nuclear paramagnetic susceptibility measurements in order to verify various predictions of the theory. One of these concerns the strictly asymptotic temperature approach of the nuclear paramagnetic susceptibility of the liquid, or the solid, toward its limiting ideal Langevin-Brillouin limit. This feature of the susceptibility appears to be necessary for an explanation of the locus of the vanishing expansion coefficients located, at already moderate pressures, at relatively high temperatures, T ≳ 1.0°K. On assuming the absence of nuclear magnetic anomalies, the spin system of the solid is expected to render this phase also anomalous in its thermal properties, up to relatively high temperatures and pressures, as suggested by recent findings of two independent groups of experimental investigators in this Laboratory. Within certain relatively mild limitations, it is shown that solid He 3 may exhibit two possible types of thermal excitations of its normal degrees of freedom. One of these, denoted as case (a), corresponds to excitations which appear to be particle like, as those of the liquid all over its phase diagram. They impose at low temperatures negative latent heats in the solid-liquid phase change, through the dominance of the entropy decrease of the nuclear spin system in this transformation. In case (b), phonon types of thermal excitations appear to be allowed, provided the solid-liquid phase separation line has a positive though small temperature slope at low temperatures. The importance of the indicated empirical decision between these two types of thermal behaviors for the theory of the dense phases of He 3 hardly needs to be emphasized.